Column Buckling Calculator

Inputs

End condition

Boundary condition used for the effective length K*L.

Unsupported length (L)

Unbraced column length between end restraints.

Young's modulus (E)

Steel is about 200 GPa; aluminium about 69 GPa.

GPa

Section input

Use a solid round diameter, or enter known area moment of inertia and area.

Round diameter (d)

Solid round column diameter. I = pi*d^4/64 and A = pi*d^2/4.

Applied axial load (P)

Compressive load to compare against the Euler critical load.

Default result

Euler critical load(Pcr)

37,850N

Pass

37.85 kN · 8,509 lbf

Pinned - pinned (K = 1.0) gives K = 1.

Pcr = pi^2*E*I/(K*L)^2.

Also computed

Load / Pcr(P/Pcr)0.2642

Applied compressive load divided by Euler critical load.

Effective length(K L)1,000mm

Slenderness ratio(K L / r)160

Euler stress(Pcr/A)77.11MPa

Radius of gyration(r)6.25mm

Area moment of inertia(I)1.917cm⁴

Method notes 4 notes

Euler buckling load is Pcr = pi^2*E*I/(K*L)^2, where K*L is the effective length for the chosen end restraint.
Use the least moment of inertia I about the weak buckling axis. Slenderness is K*L/r, where r = sqrt(I/A).
Euler is an elastic long-column check. Short or intermediate columns need a yield/Johnson or code-based check, and real end fixity usually sits between ideal cases.
Initial crookedness, eccentric load, side load, local wall buckling and connection strength are not included.